\section{Introduction to the study}
Modeling weather dynamics requires a thorough understanding of the field and its underlying physical processes. The chaotic nature of these systems entails the main obstacle to accurately map the evolution of meteorological configurations, especially when considering small-scale events.\\
Looking instead at large-scale patterns allows to enlarge the forecasting window beyond some few days, and it could be also useful to track phenomena at the finer-grained level. In this context, weather regimes still represent a partially explored branch of meteorology, while being some of the main drivers and source of variability in the climatic conditions.\\
Despite their recurrent and quasi-stationary nature, the innermost difficulty is to properly recognize them, and, consequently, quantifying the impact of each of these physical configurations.\\
Application domains beyond meteorology are pervasive in daily life scenarios, among which the energy sector stands out, with a particular emphasis on energy trading activities. To render the idea, some of the main influenced factors are:
\begin{itemize}
    \item production: this is especially true when dealing with renewable energy systems, like solar, wind power and hydro-electric productions
    \item transport: many goods are still transported over rivers, such as LNG (Liquid Natural Gas). The monitoring of water-levels is thus central, being highly correlated with meteorological phenomena like precipitations, snow melting, temperatures etc.
\end{itemize}
and, more generally
\begin{itemize}
    \item the demand and consumptions of end-customers, influencing the \textit{base} and \textit{peak} loads, and thus the necessity for an energy producer/seller/provider to intervene on the market
\end{itemize}
Hence, the possibility to accurately predict (up to a certain extent) meteorological patterns represents a possibility to build weather-driven financial strategies with some anticipation.\\
In this context, systems of physical equations, while central in tracking the short-term dynamics, are of limited effectiveness, being strongly sensitive to the initialization conditions. Therefore, we recur to the means of statistical learning techniques, as a trade-off offering cheaper computation, better performances, while preserving an overall higher interpretability of the dynamics. Also, we extend our focus on the medium-term range (sub-seasonal), possibly entailing a ``window of opportunity'' for energy trading applications we aim to encompass. Thereby, we are interested in giving a proper quantification of energy variables, strictly dependent on the regimes recognition task. Finally, we leverage on this knowledge to perform sub-seasonal forecasts, trying to catch signal up to 40 days with anticipation.\\
Our study is mostly focused on the North-Atlantic European region, during the winter period. However, the pipeline we develop is highly portable, and easily adaptable to different input data typologies, as well as to different geographic zones and seasons.\\
The dissertation is organized as follows: in Section \ref{sec:history} an introduction to energy markets is presented, together with the main financial instruments adopted in the setting;  Section \ref{sec:weather_variables} outlines the most relevant energy variables employed in the project, and firstly introduces the concept of \textit{weather regimes}. Chapter \ref{chap:data} gives an overview of the main datasets used across the study, as well as presenting the data pre-processing techniques conceived for the project (Section \ref{sec:preproc}). Subsequently, Chapter \ref{chap:models} covers an extensive dissertation on the Machine Learning algorithms used to cluster weather regimes, as well as presenting the experimental campaign from Section \ref{sec:results} on. Finally Chapters \ref{chap:quant} and \ref{chap:forecasts} integrate the two final steps of the pipeline, respectively discussing the statistical assessment and forecasting procedures we have performed in the energy domain.
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after a general overview on the of how power markets (Section \ref{subsec:history}), a more in-depth description of weather variables is presented (Section \ref{sec:weather_variables}). Subsequently, the experimental setup is described, from the data sources (Section \ref{sec:data}), to the modeling frameworks (Section {\ref{sec:models}}) and the description of the results.\\
Finally, we draw some conclusions \dots
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